Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the zeros for the function  using a graphing
calculator. a. | (10, 0) and (6, 0) | c. | (–4, 0) and (–8, 0) | b. | (–10, 0) and
(–6, 0) | d. | (–4, 0)
and (8, 0) |
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2.
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Determine the zeros for the function  using a graphing
calculator. a. | (6, 0) and (–6, 0) | c. | (0, 7.22) and (0,
4.78) | b. | (24, 0) and (6, 0) | d. | (4.78, 0) and (7.22, 0) |
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3.
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Which function represents  written in standard form?
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4.
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Which equation represents the equation of a quadratic function in vertex form
whose vertex is at (-2, 2) and that passes through (–3, –3)?
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5.
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Which graph represents the function  ?
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6.
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A quadratic function has zeros at –1 and 3 and passes through the point
(4, 5). Which equation represents the function in vertex form?
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7.
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What is the factored form of 
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8.
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Which equation represents  in vertex form?
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9.
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Determine the values of a, h¸and k that make the
equation  .
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10.
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Determine which coordinate is the vertex of  without graphing
the parabola. a. | (5, 35) | c. | (–5, –40) | b. | (–5,
35) | d. | (–5,
10) |
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11.
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A manufacturing company has a profit, M( x), that can be modelled
by  , where x is the cost of the objects that
they manufacture. What should the company charge to maximize the profit? a. | $6.50 | c. | $65 | b. | $25 | d. | $17 112.50 |
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12.
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What information can you gather immediately from a quadratic function written in
standard form?
a. | vertex | c. | y-intercept | b. | equation of the axis of
symmetry | d. | domain |
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13.
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A quadratic equation cannot have how many real solutions?
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14.
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Identify the values of a, b, and c you would use to
substitute into the quadratic formula to solve  . a. | a = –5; b = 3; c = –3 | c. | a = 1; b = –5;
c = –18 | b. | a = 1; b = 5; c =
–18 | d. | a = 1;
b = 1; c = –12 |
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15.
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Use the quadratic formula to solve  . Round your answer to two
decimal places. a. | –5.43 and 1.93 | c. | –4.5 and 0.98 | b. | –1.93 and 5.43 | d. | no real
solution |
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16.
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Set up the quadratic equation for  .
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17.
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Determine the roots of  to the nearest hundredth. a. | 11 | c. | 2 and 11 | b. | –11 | d. | no real
solution |
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18.
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A golf ball is chipped out of a sand trap along a path that can be modelled by
the quadratic function  , where time, t, is in seconds and height,
h( t), is in metres. Use the quadratic formula to determine where the ball will land to
the nearest hundredth. a. | 0 m | c. | 7.26 m | b. | 4.81 m | d. | 88.47 m |
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19.
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All of the following are ways to determine the roots of a quadratic function
except:
a. | graphing | c. | completing the square | b. | finding the
discriminant | d. | quadratic
formula |
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20.
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Determine the discriminant of  .
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21.
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Use the discriminant to determine the number of roots of  .
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22.
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Use the discriminant to determine the number of roots of  .
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23.
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For what value(s) of t does the function  have no
zeros? a. | t = 12 | c. | t < 12 | b. | t > –12 | d. | –12 < t <
12 |
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24.
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Which discriminant indicates that a quadratic function has two distinct real
solutions and the function has two x-intercepts?
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25.
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The graph shows the height of a ball thrown into the air, where time, t,
is in seconds and height, h( t), is in metres. Using the graph shown below, what is the
algebraic model? 
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26.
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The graph shows the height of a baseball thrown into the air, where time,
t, is in seconds and height, h( t), is in metres. Using the graph shown below,
what is the algebraic model? 
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27.
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A disc is thrown into the air and follows a path modelled by the function  , where time, t, is in seconds and height, h( t), is in metres. When
does the disc hit the ground again? a. | 1.0 s | c. | 2.8 s | b. | 1.4 s | d. | 3.0 s |
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28.
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The cost of running a carwash is a function of the number of cars washed per
hour. The cost function is  , where C( x) is the cost in dollars,
and x is the number of cars washed per hour.Determine the level of approximate number of cars
per hour is most economic. a. | 3 cars/h | c. | 12 cars/h | b. | 5 cars/h | d. | 25 cars/h |
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29.
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An amusement park usually charges $34 per ticket, but wants to raise the price
by $1 per ticket. The revenue that could be generated is modelled by the function  ,
where x is the number of $1 increases and the revenue, R( x), is in dollars. What
should the ticket price be if the park wants to earn $15 000?
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30.
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Jeremiah is going to enclose a portion of his backyard with a fence for his
dogs. He has 48 metres of fence. The area that can be enclosed by the fence is modelled by the
function  , where x is the width of the area in metres
and A( x) is the area in square metres. What is the maximum area that can be
enclosed?
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31.
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The population of a city can be modelled by the function  ,
where x is the number of years since 2000. According to the model, when will the population be
the lowest?
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32.
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The population of a village can be modelled by the function  ,
where x is the number of years since 1990. According to the model, when will the population be
the highest?
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33.
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Curves of good fit are useful for
a. | predicting the future | b. | solving problems involving the
relationship | c. | extrapolating | d. | interpolating |
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34.
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Determine the equation of the parabola shown in the graph below. 
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35.
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Determine the equation of the curve of good fit for the scatter plot shown
below. 
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36.
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A quadratic function has a vertex located at (6, –6) and a
y-intercept of 12. Which equation represents the function in standard form?
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37.
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Determine the equation of the curve of good fit in standard form that represents
the data in the table. | Ticket Price ($) | 1.50 | 2.00 | 2.50 | 3.00 | 3.50 | 4.00 | | Profit ($) | 16.88 | 22.00 | 26.88 | 31.50 | 35.88 | 40.00 | | | | | | | |
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38.
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Determine the equation of the curve of good fit in vertex form the represents
the data in the table. | Time (s) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | | Height (m) | 18.8875 | 34.875 | 47.3875 | 57.8875 | 65.8875 | 71.3875 | | | | | | | |
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39.
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A quadratic function passes through the points (–3, 18), (–1, 18),
and (1, 2). Determine its equation algebraically without using quadratic regression.
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Short Answer
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40.
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Write the equation for the function shown in the graph below in vertex
form. 
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41.
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Write the equation of the quadratic function in vertex and standard form whose
vertex is at (–1, 6) and that passes through (2, 24).
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42.
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What number must you add to  to create a perfect
square?
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43.
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Factor  .
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44.
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Identify the values of a, b, and c you would substitute
into the quadratic formula to solve  .
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45.
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Identify the values of a, b, and c you would substitute
into the quadratic formula to solve  .
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46.
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The quadratic function  models the flight of a model
rocket, where the height, h( t) is in metres, and the time, t is in seconds. How
long will the rocket be in the air?
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47.
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Write the discriminant of  . Do not evaluate.
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48.
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Determine the number of real solutions of the quadratic equation  . Do
not solve.
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49.
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For what value(s) of a does the function  have two
zeros?
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50.
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The profit of a company is modelled by the quadratic function  ,
where the profit, P( x), is in x dollars. What is the maximum profit?
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51.
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Determine the equation of the parabola shown in the graph below. 
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Problem
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52.
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A ball is launched by a catapult into the sky. The path of the ball can be
modelled by the function  , where height, h( t), is in metres
and time, t, is in seconds. a) When does the ball reach maximum height? Why is it a
maximum? b) What is the maximum height reached by the ball?
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53.
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Describe how you can immediately determine the vertex of a parabola when the
function is written in vertex form.
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54.
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Complete the square to express  in vertex form. Graph the
function. State the domain and the range of the function.
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55.
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Complete the square to express  in vertex form. Graph the
function. State the domain and the range of the function.
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56.
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a) Explain how you would solve this problem: For what value of n does the
function  have only one zero? b) Use your strategy to
find the value of n.
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57.
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a) Explain how you would solve this problem: For what value of q does the
function  have two distinct real zeros? b) Use your
strategy to find the value of q.
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58.
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The height of a baseball hit into the air is given by the quadratic equation
 , where time, t, is in seconds and height, h( t), is in metres. a)
What was the height of the ball when it was hit? b) What is the maximum height of the ball? c)
Is the ball still in the air after 4 s? Explain. d) When is the ball at a height of 24 m?
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59.
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The height of a football being punted is given in the table. | Time (s) | 0 | 0.25 | 0.5 | 0.75 | 1.0 | 1.25 | | Height (m) | 0.89 | 7.2 | 12.89 | 17.95 | 22.39 | 26.2 | | | | | | | |
a) Determine the equation for
a curve of good fit for the data in the table. b) State any restrictions on the domain and range
of your model. c) Use it to predict when the ball will hit the ground.
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60.
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The height of a disc being thrown is given in the table. | Time (s) | 0 | 1 | 1.5 | 2 | 2.5 | 3 | | Height (m) | 0.55 | 12.55 | 14.8 | 14.55 | 11.8 | 6.55 | | | | | | | |
a) Use
your graphing calculator to create a scatter plot. b) Estimate the coordinates of the
vertex. c) Write the function that defines the curve of good fit. d) State any restrictions on
the domain and range of your model.
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